Jim Walsh receives Oberlin Research Status Award
Jim Walsh recently received a coveted Research Status Award from Oberlin College. This award provides for full salary for the 2016-17 academic year with no teaching obligations, so that Jim can focus solely on his ongoing research in the mathematical modeling of paleoclimate. (Research Status Awards at Oberlin occur between sabbaticals.) Applications for Research Status Awards are evaluated both externally and internally on the quality of the proposed research. Jim is grateful for the wonderful support provided by MCRN generally, and for the encouragement and support provided by members of MCRN’s PaleoSeminar in particular. He states,"This award would not have been possible without my involvement in and support from MCRN!"
Q. Please tell us a bit about your career path.
My path to becoming an academic has been somewhat nonlinear. Upon completing my undergraduate studies as a mathematics major at the University of Connecticut, I joined the United States Peace Corps. As a Peace Corps Volunteer, I taught mathematics in a lycée (secondary school level) for two years in Togo, West Africa. Returning to the Unites States, I subsequently taught mathematics for three years in a public high school. It was at this point, desiring more of an intellectual challenge and missing the study of mathematics, that I began my graduate studies in mathematics at Boston University; I obtained my PhD in 1991 from the age of thirty-four. I became a member of the Mathematics Department at Oberlin College in 1991, where I am now set to begin my twenty-fifth year.
Q. How did you become involved in MCRN?
I spent a 2011-12 sabbatical year as a Visiting Professor in the School of Mathematics at the University of Minnesota, where Dick McGehee, a founding Principal Investigator in MCRN and a renowned expert in dynamical systems, leads a research group to bring techniques from dynamical systems to bear on problems arising in climate modeling. I was completely hooked! I am also delighted to add that my thesis advisor, Dick Hall, was a student of Dick McGehee.
Q. Please tell us about your research.
My climate modeling research concerns questions arising in the study of paleoclimate. Has the Earth been completely ice-covered in its past (a snowball Earth episode), for example? If yes, what eventually caused the ice to retreat? Why did the occurrence of ice ages switch from a period of roughly 40,000 years to 100,000 years during the mid-Pleistocene, leading to longer and colder ice ages over the past one million years? Questions such as these, of course, are not merely academic in nature: One looks to the past to gain insight into the future evolution of climate on Earth. An understanding of the increase in temperature and rapid rise in atmospheric CO2 concentrations during the Paleocene-Eocene Thermal Maximum, for example, might help better predict (and mitigate) current anthropogenic contributions to climate change.
I focus in particular on the mathematical analysis of conceptual climate models, which provide a broad view of the way in which a specified system variable, such as surface temperature, depends upon a few prominent climate components. (Belying their simplicity, conceptual climate models play a vital role in climate science.) I wrote a paper with colleague Esther Widiasih in which we analyzed an infinite-dimensional integro-differential system, arising from a model of latitude-dependent surface temperature and ice sheet interactions. We proved the existence of a stable Jormungand state, an alternative to a snowball Earth episode in which the advance of the ice sheet halts in tropical latitudes, shy of the equator.
With student Chris Rackauckas, I analyzed a finite-dimensional approximation to the model mentioned in the above paragraph, leading to what is known as a nonsmooth system. We proved the existence of a stable Jormungand state for the approximating system as well, using techniques from the still-developing field of nonsmooth dynamical systems.
In my most recent work, joint with Esther Widiasih, Jon Hahn and Dick McGehee, we present and analyze a new model of the glacial/interglacial cycles. This model leads to a nonsmooth system of differential equations in three dimensions having a plane of discontinuity. We prove the model has an attracting periodic orbit, corresponding to the advance and retreat of the ice sheets over long time scales. In future work we plan to incorporate Milankovitch forcing into the model in an effort to better understand the mechanisms underlying the glacial/interglacial cycles.
J.A. Walsh and R. McGehee, Modeling climate dynamically, The College Mathematics Journal, 44 (5) (2013), 350-363. (A special issue devoted to the Mathematics of Planet Earth.)
J.A. Walsh and E. Widiasih, A dynamics approach to a low order climate model, Discrete and Continuous Dynamical Systems -- Series B, 19 (1) (2014), 257-279.
J.A. Walsh and C. Rackauckas, On the Budyko-Sellers energy balance climate model with ice line coupling, Discrete and Continuous Dynamical Systems -- Series B, 20 (7) (2015), 2187-2216.
J.A. Walsh, Climate modeling in the sophomore-level ODE course, The Journal of Undergraduate Mathematics and its Applications, 36 (4) (2015).
J.A. Walsh, E. Widiasih, J. Hahn and R. McGehee, Periodic orbits for a discontinuous vector field arising from a conceptual model of glacial cycles, submitted.